The Fission Myth

Written: 1998.11.08Last Revised: 1999.04.25

Some trekkies have advanced the theory that the Death Star caused
all of the fissionable elements in Alderaan to undergo fission at
once. This is basically a permutation of the idea that all of the
energy came from the target rather than the source. However, there
are only a few possible modes of nuclear fission. Of these, the most
common (and applicable) is neutron capture followed by spontaneous
fission. This is the mechanism used in atomic bombs and 20th century
nuclear fission reactors. Photo-disintegration (absorption of a
highly energetic gamma ray, which excites the nucleus to a state
where the nuclear binding force is overcome) or extreme high-energy
collision (such as the particle collisions in a large particle
accelerator) can cause nuclei to fission, but they cannot produce
net-positive power- photo-disintegration consumes power
because it is only effective on small nuclei so it results in an
increase in energy states, and extreme high-energy collision
requires so much energy on the part of the impactor that the energy
yield doesn't make up for the cost. Therefore, we will discuss
nuclear fission through neutron capture.

The basic theory is simple: bombard low-stability heavy metals
such as uranium with neutron radiation, and some of the neutrons
will be captured. Once they have been captured, the result is a
compound nucleus in an excited state. This state of excitation,
combined with the Coulomb repulsion between the protons in the
nucleus, is enough to overcome the strong nuclear forces holding the
nucleus together. As a result, the nucleus splits apart into two
smaller nuclei.

Why do heavy metals easily undergo fission? It happens because of
the curve of binding energy per nucleon. Although binding energy
climbs steadily with increasing atomic number, binding energy per
nucleon only climbs until it reaches a peak between nuclei
containing between 50 and 80 nucleons. After this peak, it begins to
drop off again. As a result, the ratio between Coulomb repulsion and
nuclear binding force can approach unity with certain heavy metal
isotopes. If those isotopes are made to oscillate violently (by the
addition of a neutron, for example), then the oscillation may
distort the shape of the nucleus enough that Coulomb repulsion can
literally tear the atom apart from within, in spite of the nuclear
binding force.

U-235 is highly susceptible to nuclear fission because low-energy
neutrons (so-called "thermal neutrons") can cause fission
due to its high ratio of protons to neutrons. However, it is an
extremely rare isotope of uranium, comprising less than 1% of
the total supply on Earth. U-238 is by far the most common isotope
of uranium, but it is not easily fissioned. High-energy neutron
radiation (~1.3 MeV or higher) is required to induce fission in
U-238, which is why refined uranium (with increased levels of U-235,
up to 4.5% for power plants and 90% for weapons) has always been
used in weapons and most types of nuclear power plants. The Canadian
CANDU nuclear reactor system is currently the only major nuclear
reactor design in the world which can run on unrefined
uranium, thanks to the superior effectiveness of its heavy-water
moderator.

However, this is all essentially background trivia. In order to
induce complete fission in the uranium atoms scattered through the
mass of a planet, the Death Star would have to subject the entire
planet to an intense neutron radiation flux, which is impractical
for numerous reasons:

Exothermal nuclear fission chain
reactions are not possible because they require proximity of
reactant. The fissionable material in a planetary body is scattered
throughout the planet's mass, rather than being concentrated in one
place.

Since exothermal nuclear fission
chain reactions are not possible in the widely dispersed
fissionable materials in a planetary mass, the theoretical neutron
beam would have to directly strike the entire planetary mass
(ie- it couldn't simply hit the planet in one spot and start a
chain reaction).

A neutron beam cannot directly
affect the mass of a planet without having to move through most of
the planet (eg- how can it affect the far side of the planet
without going through the near side?), and neutrons are much too
massive to move so easily through such a large volume of material.

Neutrons cannot be programmed to
"seek out" fissionable elements like U-238, so they will
simply hit whatever is in front of them. This means that the
neutron beam would have to hit most or all of the atoms in the
planet, including those which are either non-fissionable or
endothermal in fission. There is no way to restrict the neutron
beam so that it hits just the fissionable materials.

All of the above restrictions mean that the hypothetical
fission-inducing beam would have to carry enough energy to induce
an intense flux of 1MeV neutrons, ideally carrying enough neutrons
to hit all of the atoms in the entire planet. However, such a
neutron beam would have to contain ~1E50 neutrons, for a total
energy requirement of more than 1E37 joules. Furthermore, this
figure assumes perfect efficiency, ie- all of the neutrons strike
their targets with enough energy to induce fission!

Is it possible to induce fission in the fissionable materials
scattered throughout a planet's mass? Yes, given some extreme
hypothetical situations. But would the fission produce more energy
than the neutron beam required to induce fission? No. The neutron
beam (in addition to having a completely different appearance than
the superlaser in ANH) would need to carry so much energy that
fission would be utterly redundant and insignificant. Therefore,
nuclear fission utterly fails as an explanation for the Death Star's
destruction of Alderaan.

As a final note, it is worth mentioning that a planetary core is
not composed mostly of heavy metals, contrary to some popular
beliefs. It is composed mostly of iron. The Earth's chemical
composition, by mass, in decreasing order, is:

Iron

34.6%

Oxygen

29.5%

Silicon

15.2%

Magnesium

12.7%

Nickel

2.4%

Sulfur

1.9%

Titanium

0.05%

Note that every one of those elements is a fairly stable, light
element, with atomic numbers between 8 and 28. This is hardly
surprising. Although the universe does contain heavy
fissionable elements, those elements are present in extremely
small quantities.

The Fusion Myth

Naturally, since fission is infeasible on a planetary scale
because of the inherent difficulties and the rarity of easily
fissioned materials in a planet's mass, some trekkies turn to fusion
as an alternate explanation (anything would apparently be better
than simply admitting that it is impossible to blow a planet apart
without using a staggering amount of energy). Nuclear fusion
produces more energy per unit mass than nuclear fission. While the
theoretical energy density for perfect fission is roughly 8.5E13
J/kg, the theoreteical energy density for perfect fusion is roughly
6.3E14 J/kg, an increase of more than 7 times.

However, nuclear fusion is even more difficult to induce than
nuclear fission. It occurs naturally in stars, but a star must
compress and heat hydrogen plasma to temperatures in excess of 15
million K and pressures in excess of 250 billion bars (25 billion
MPa). At these temperatures and pressures, the hydrogen plasma is
compressed to roughly 1.5E5 kg/m³, which is 13 times the
density of lead. Note that it is still gaseous at this
density! The temperature and pressure increase the frequency and
velocity of proton-proton collisions to the point that some of those
collisions will occur at sufficient speed to overcome Coulomb
repulsion and cause nuclear fusion. The hydrogen-hydrogen fusion
reaction is but the first stage of a three-stage fusion reaction. In
the first stage, four hydrogen ions fuse to form two deuterons, two
positrons, and two neutrinos. In the second stage, the deuterons
from the first stage fuse with two more hydrogen ions to form two
helium atoms (He3) and two gamma rays. In the third stage, the two
He3 ions from the second stage fuse to form a heavier helium isotope
(He4), plus two hydrogen ions. The net result is that four hydrogen
ions turn into an alpha particle (He4) and two positrons, with a
total energy release of approximately 26.2 MeV.

However, the reaction rate of nuclear fusion in the sun's core is
extremely low. In spite of the enormous temperatures and pressures,
the sun only produces ~1E12 kg/s of deuterium per second, because
only one in 1E26 proton-proton collisions will result in fusion. In
other words, the sun's reaction rate is so low that only 1/2E18 of
its mass reacts each second! This is very fortunate for the people
of Earth, otherwise the sun's lifespan would be greatly shortened
and its intensity would be far too high for any terran life forms to
survive. However, this does indicate the difficulty of inducing
fusion in hydrogen- even at such enormous temperatures and pressures
as those found in the sun's core, fusion occurs at infinitesimally
slow rates. It is only the sheer size of the sun that causes
its large overall power output.

So, how difficult would it be to induce fusion in the hydrogen
scattered throughout an Earth-like planet's mass? First, the amount
of hydrogen in the Earth's crust is insignificant relative to its
mass- less than 4E19 kg out of the total 6E24 kg. Furthermore, all
of the Earth's hydrogen is in its crust- the mantle and core are
composed of heavier elements like iron. Therefore, we can easily
determine the difficulty of producing the necessary conditions to
duplicate the hydrogen particle density and temperature in the core
of the sun, to induce fusion. Obviously, we know that we need to
heat the entire planet to more than 15 million K if we are to
achieve fusion-generating temperatures. But we also know that
we need an average hydrogen atom density of roughly 1.5E5
kg/m³ (the density of other materials is meaningless, because
fusion rates are based on reactant density), so all of an
Earthlike planet's 4E19 kg of hydrogen would have to be compressed
into a sphere of less than eighty kilometres diameter!
Furthermore, since there is no conceivable way for the Death Star
beam to gather all of a planet's hydrogen, compress it, and then
teleport it to the centre of the planet to create the necessary
expansion dynamics, the Death Star could only accomplish this feat
in one of two ways:

Compressing the entire planet
into an 80 kilometre wide sphere somehow, so that the hydrogen
atoms are close enough to each other to react. This is clearly
ludicrous- if the Death Star heated the planet to 15 million K and
compressed it to less than a millionth of its original volume, this
would have been more difficult than simply blowing it apart.
The final nail in the coffin for this theory is the fact that even
if this were somehow achieved, we would only be duplicating
the conditions in the sun, so we would only get the sun's fusion
reaction rate. We need far more than the sun's fusion
reaction rate to generate planet-destroying energy in a fraction of
a second, particularly when we have to work with a quantity of fuel
(hydrogen in Earth's crust) that is far smaller than the amount of
fuel available in the sun's core. Remember: the entire power
output of the Earth's sun would be insufficient to destroy a
planet with a 1-second blast. In fact, it would take more than five
hundred thousand times the power output of the Earth's sun to
even approach the lower limit for a Death Star blast.

Employing the principle of inertial-confinement fusion
to compress the hydrogen. Inertial-confinement fusion has been
researched by 20th century Earth scientists using lasers to
detonate solidified deuterium-tritium pellets, but the very concept
of the method is inherently inapplicable to Alderaan. Inertial
confinement fusion is based on the principle that if a pellet of
deuterium-tritium is blown apart at incredible speed, the inertial
resistance of the outer layers will create enough internal pressure
to achieve fusion. Therefore, the Death Star could only achieve
inertial-confinement fusion in Alderaan by blowing the planet apart
at incredible speed. Obviously, if the Death Star has to
blow the planet apart at incredible speed in order to ignite
fusion, then the energy from fusion is redundant because the planet
is already being blown apart! The final nail in the coffin
for this theory is that massive pulse lasers are required to induce
fusion in a pellet of laboratory-pure deuterium and tritium, but
almost all of the hydrogen in an Earth-like planet will be in the
form of H1, not deuterium or tritium. Hydrogen is an order of
magnitude less suitable for fusion than deuterium or
tritium.

The conclusion to this section is similar to the conclusion for
the fission section. Is it possible to induce fusion in the hydrogen
molecules scattered through the crust of a planet? Yes. But would
this fusion produce more energy than the energy required to induce
fusion in the first place? Absolutely not.